CN110515152B

CN110515152B - hollow core fiber

Info

Publication number: CN110515152B
Application number: CN201910726477.0A
Authority: CN
Inventors: 弗朗西斯科·波莱蒂; 赛义德穆罕默德·阿博哈密·穆萨维
Original assignee: University of Southampton
Current assignee: University of Southampton
Priority date: 2014-06-06
Filing date: 2015-06-08
Publication date: 2021-08-10
Anticipated expiration: 2035-06-08
Also published as: EP3249432B1; JP2020016891A; EP3249431B1; JP6876762B2; WO2015185761A1; US20170160467A1; EP3249432A1; SG11201610233XA; EP3152607B1; DK3152607T3; US20190101695A1; US12117646B2; GB201410100D0; EP3152607A1; DK3249432T3; HK1245894A1; DK3249431T3; CN110515152A; GB2526879A; US10139560B2

Abstract

An anti-resonant hollow core fiber comprising a first tubular cladding element, a plurality of second tubular elements, and a plurality of third tubular elements, the first tubular cladding element defining an inner cladding surface, the second plurality of tubular elements attached connected to the cladding surface and defining therewith a core having an effective radius, the second tubular elements are spaced apart with a space between adjacent ones, and each of the plurality of third tubular elements are each nested in a corresponding second tubular element.

Description

Hollow core optical fiber

The present application is a divisional application of the following applications: application date: 2015, 6 months and 8 days; application No.: 201580042024.6, respectively; the invention relates to a hollow fiber.

The present invention relates to hollow core optical fibers, in particular antiresonant fibers, especially ultra low loss fibers, broad bandwidth fibers, single mode hollow core fibers and high birefringence (Hi-Bi) fibers.

Hollow core optical fibers have been studied and developed for nearly eighty years. Theoretically, these fibers can achieve ultra-low propagation loss and nonlinearity by guiding light in air rather than in solid materials, and can also provide much higher propagation velocities (i.e., shortened delays) and laser damage thresholds than all-solid fibers. However, in practice, the losses cannot be reduced to a level comparable to-0.15 db/km that can be achieved with all-glass fibers, which has prevented the widespread use of hollow core technology.

There are two main types of single-material hollow-core fibers, which are based on photonic band-gap guiding (photonic band-gap fibers-PBGF), or on antiresonant guiding (antiresonant fibers-ARF, such as gau fibers, "negative-curvature" fibers, simplified antiresonant fibers, and hexagonal fibers).

Photonic Band Gap Fibers (PBGF) provide the lowest loss (attenuation to 1.2 db/km at 1.62 pm wavelength-ultralow loss for hollow core photonic crystal fibers as noted by Roberts et al, optical courier, pages 236 to 244, phase 13, 2005), but over a narrow bandwidth (10-30% of the central wavelength), while antiresonant fibers (ARF) provide a bandwidth amplification factor 2 to 10 times that of Photonic Band Gap Fibers (PBGF), with higher direct loss and more pronounced bend sensitivity.

In photonic band gap fibers, steering is achieved by antiresonance from an array of ordered and appropriately sized rods within the cladding. Since the number of rods in the radial direction can be increased at will, the leakage or confinement losses can be made arbitrarily small. However, the rods need to be interconnected by thin glass struts, which do not operate at the optimum anti-resonance.

Thus, the glass boundary, which is inherently rough (at least at the atomic/molecular level), cannot effectively repel electromagnetic fields, and this produces surface scattering, which is the major source of loss in photonic band gap fibers.

In contrast, in antiresonant fibers, antiresonance comes from uniformly sized glass struts that surround a core that confines light in air. Since the legs effectively repel light, scattering losses are generally negligible in antiresonant fibers. However, none of the arrangements that have been devised allow multiple layers to coherently reflect light that tends to leak out of the core. Therefore, in the antiresonant fiber, leakage loss is dominant. Another point with anti-resonant fibers is the presence of nodes formed at the junctions between glass struts, especially those nodes having different and varying thicknesses, and introducing stray and spectrally dense resonances in the anti-resonant region, thereby increasing losses.

Fibers have been developed to address this problem by forming a core that is surrounded by a "negative curvature" so that the nodes are pushed farther away from the air-guided mode.

In addition, a fiber was developed that could completely remove unwanted nodes by creating a grid that did not touch the tube (2013, volume 21, optical express, pages 9514 to 9519, Kolyadin et al). The nodeless tube lattice of such fibers comprises a silicon ring comprising eight anti-resonant elements at the surface of the cladding, each element in a contactless relationship, representing the state of the art in terms of the anti-resonant fibers produced, showing a transmission band in the spectral range from 2.5 to 5 microns, with a minimum loss level of 4 to 5 db/m, an average loss of 30 db/m at 5.8 microns and 50 db/m at 7.7 microns, respectively.

However, in such fibers, the confinement loss is still much higher than the scattering loss. The reason for this is that the light confinement is effectively created by only one glass pillar that is azimuthally oriented via two fresnel reflections at the glass-air boundary.

More recently, a nodal antiresonant fiber has emerged (Belardi et al, pages 1853-1856 of optics letters 39, 2014) comprising a silicon ring including eight primary antiresonant elements at the cladding surface, each element in contacting relationship, with at least one other antiresonant element nested within each primary antiresonant element.

The present invention is directed to an improved fiber structure, and in particular, an innovative fiber structure that provides attenuation losses comparable to or lower than photonic band gap fibers and a bandwidth as wide as that of antiresonant fibers.

In one aspect, the present invention provides an antiresonant hollow-core fiber comprising a first tubular cladding element defining an inner cladding surface, a plurality of second tubular elements attached to the cladding surface and defining therewith a core having an effective radius, the second tubular elements being spaced apart with a spacing between adjacent ones of the second tubular elements, and a plurality of third tubular elements each nested within a respective one of the second tubular elements.

In one embodiment, the second tubular elements are arranged in symmetrical relationship at the cladding surface.

In one embodiment, the first tubular element is circular in cross-section.

In one embodiment, the second tubular element is circular in cross-section.

In another embodiment, the second tubular element has a longer dimension in the radial direction than in the tangential direction, optionally an elliptical or oval cross-section.

In one embodiment, one or more of the tubular elements have different cross-sectional shapes.

In one embodiment, the tubular element is made of glass, optionally silicon.

In one embodiment, the tubular element is made of glass having a refractive index of at least about 1.4, optionally, from about 1.4 to about 3, optionally, from about 1.4 to about 2.8.

In one embodiment, each of the second tubular elements is attached to the first tubular element at only a single location of the cladding surface.

In one embodiment, the third tubular elements are each attached to a respective second tubular element at the location where the second tubular element is attached to the cladding surface.

In one embodiment, the ratio of the spacing of adjacent second tubular elements to the wall thickness of the second tubular elements is greater than about 0.5, optionally, greater than about 0.8, optionally, greater than about 1, and optionally, greater than about 2.

In one embodiment, the ratio of the spacing of adjacent second tubular elements to the wall thickness of the second tubular elements is less than about 12, optionally less than about 10, optionally less than about 8, and optionally less than about 6.

In one embodiment, the second and third tubular elements have substantially the same wall thickness.

In one embodiment, the ratio of the radial spacing of the radially inner walls of the second and third tubular elements to the radius of the core is between about 0.3 and about 1.0, optionally between about 0.35 and about 0.95.

In another embodiment, the ratio of the radial spacing of the radially inner walls of the second and third tubular elements to the radius of the core is between about 0.05 to about 0.4, optionally between about 0.1 to about 0.3, optionally between about 0.2 to about 0.3.

In yet another embodiment, the ratio of the radial spacing of the radially inner walls of the second and third tubular elements to the core radius is between about 0.8 and about 1.2, optionally between about 0.9 and about 1.2, optionally between about 1.0 and about 1.2.

In one embodiment, the fiber has a fundamental loss of less than 0.15 db/km at a wavelength between about 1.0 pm and about 2.5 pm.

In another embodiment, the fiber has a fundamental loss of about 1 dB/km at wavelengths up to about 2.7 pm.

In yet another embodiment, the fiber has a fundamental loss of less than 1 dB/m at wavelengths up to about 5 microns.

In yet another embodiment, the fiber has a fundamental loss of less than 4 db/m at wavelengths up to about 7 microns.

In yet another embodiment, the fiber has a fundamental loss of less than about 1 dB/km at wavelengths down to about 0.8 pm.

In one embodiment, the portion of optical power directed by the fiber of material having the tubular element is less than about 1x10^-3Alternatively, less than about 1x10^-4。

In one embodiment, the core radius is optionally less than about 50 microns, optionally less than about 40 microns, optionally less than 30 microns, optionally less than about 25 microns, optionally less than about 20 microns, optionally less than about 15 microns, optionally less than about 13 microns.

In one embodiment, the fiber comprises six nested tubular elements.

In another embodiment, the fiber comprises three, four or five nested tubular elements.

In one embodiment, the fiber exhibits an effective single mode.

In one embodiment, the difference between the fundamental mode and the lowest-loss high-order mode is at least an order of magnitude, optionally at least two orders of magnitude.

In one embodiment, the nested arrangement of tubular elements supports a mode having an effective index (neff) that has an effective mode difference (Δ neff) of less than about 0.001 compared to a high order mode in the core.

In one embodiment, the fiber allows for the selection of any Mode Field Diameter (MFD) at any given wavelength.

The invention also extends to combining, optionally directly splicing, the above-described fibres with solid fibres, wherein the hollow fibres have a mode field diameter matched to that of the solid fibres.

In one embodiment, the solid core fiber is a fiber from a fiber laser, optionally an ytterbium-doped fiber laser.

In one embodiment, the difference in fundamental loss when the fiber is straight and the fiber is rolled to a diameter of 10mm is less than two orders of magnitude, optionally less than one order of magnitude, optionally less than half an order of magnitude.

In one embodiment, the fiber further comprises a plurality of fourth tubular elements, each nested within a corresponding third tubular element.

In one embodiment, the second, third and fourth tubular elements have substantially the same wall thickness.

The invention also extends to the use of the above-described fibres in an efficient single mode.

The invention also extends to the use of such fibres having any selected mode field diameter at any given wavelength.

The invention also extends to the use of the above-described fibres in a mode which reduces fundamental losses.

With the present invention, it can be expected that the total propagation loss (i.e., including scattering, confinement, bending, and material absorption losses) will be even lower than conventional telecommunications fibers, down to 0.05 db/km. This low loss, combined with low nonlinearity and wide operating bandwidth (again, wider than existing solid fibers), can provide a desirably high capacity data transmission medium.

The present invention is also directed to a high birefringence (Hi-Bi) hollow core anti-resonant fiber that is either a Polarization Maintaining (PM) fiber, i.e., that maintains the input polarization of the source signal, or a polarization (P) fiber, i.e., that introduces polarization to the source signal, e.g., that produces linearly polarized light from an unpolarized input.

High birefringence (Hi-Bi) fibers are widely used in optical communication systems, sensing and interference devices where preserving source polarization is essential. In solid core Polarization Maintaining (PM) fibers, the high birefringence effect is achieved by: applying stress or anisotropy to the fibres through the elliptical core¹However, the non-linearity of the fibers and/or the sensitivity of the fibers to external disturbances, such as temperature, can limit the performance of the manufacturing equipment (lightwave technology, volume 4, 1986, pages 1071 to 1089, polarization-maintaining fibers and their applications, Noda et al. Due to its unique low non-linearity and high sensitivity to thermal environmental changes, Hollow Core (HC) fibers can be used as a replacement in high precision sensors, for example in gas spectroscopy or in Fiber Optic Gyroscopes (FOG) (2012, volume 30, lightwave technology, pages 931 to 937, M a Terrell et al, written "fiber optic gyroscope using air core fibers"). However, high performance, low loss hollow core fibers with polarization maintaining properties are not readily available. Polarization-maintaining hollow-core fibers based on Photonic Band Gap (PBG) guiding have recently emerged (Natural communications 5, page 5085, J M Fini et al, "polarization-maintaining Single-mode Low-loss air", 2014Core fiber). In these fibers, with different guiding mechanisms, polarization-maintaining properties are typically achieved by exploiting the reverse crossing of core-cladding modes, rather than the conventional approach of solid-core fibers. However, these fibers exhibit rather high propagation losses and their operation is very sensitive to external disturbances.

The present inventors have recognized that nested anti-resonant nodeless designs allow for more control of structural parameters than photonic band gap fibers and provide improved polarization-maintaining and polarization characteristics for hollow-core fibers based on anti-resonant guiding for the first time.

In one embodiment, the wall thickness t of the at least one nested tubular arrangement of the second, outer tubular elements₁Different from the wall thickness t of at least one other nested tubular arrangement of the second, outer tubular element₂Thus, the fibers are phase birefringent and polarization maintaining and/or polarizing.

In one embodiment, the wall thickness t of the at least one nested tubular arrangement of outer tubular elements₁And the wall thickness t of at least one other outer tubular element arranged in a nested tubular manner₂Is in the relationship of 0.5t₂＜t₁＜t₂Or 1.5t₂＞t₁＞t₂Alternatively, 0.4t₂＜t₁＜t₂Or 1.4t₂＞t₁＞t₂Alternatively, 0.3t₂＜t₁＜t₂Or 1.3t₂＞t₁＞t₂。

In one embodiment, the wall thickness t of the at least one nested tubular arrangement of outer tubular elements₁And the wall thickness t of at least one other outer tubular element arranged in a nested tubular manner₂Is that t is₁＜0.9t₂Or t₁＞1.1t₂。

In one embodiment, the wall thickness of the second, outer tubular element of the first nested tubular arrangement and the second nested tubular arrangement is different from the wall thickness of the second, outer tubular element of the at least one other nested tubular arrangement.

In one embodiment, the first and second tubular arrangements are arranged in a generally opposed relationship, optionally a radial relationship.

In one embodiment, the fibers comprise two, three, four, five, six, seven or eight nested tubular arrangements.

In one embodiment, the fibers comprise four nested tubular arrangements, wherein a first pair of the nested tubular arrangements is arranged in a first substantially same direction and a second pair of the nested tubular arrangements is arranged in a second substantially same direction, the second substantially same direction being substantially perpendicular to the first substantially same direction.

In one embodiment, the effective radius of the core of the fiber is at most about 15 times, optionally at most about 7 times, optionally at most about 5 times, optionally at most about 0.5, 0.8, 1.06, 1.55, or 2 microns of the wavelength λ of the source.

In one embodiment, at least one inner tubular element, optionally the innermost tubular element, of the at least one other nested tubular arrangement has a cross-sectional size and/or shape that is different from the cross-sectional size and/or shape of the corresponding one of the at least one nested tubular arrangement, whereby the spacing Z between the one inner tubular element and an adjacent tubular element of the at least one other nested tubular arrangement₁A spacing Z between a corresponding one of the tubular elements and an adjacent tubular element other than the at least one nested tubular arrangement₂。

In one embodiment, the one inner tubular element of at least the other nested tubular arrangements has a different cross-sectional dimension.

In one embodiment, at least one other nested tubular arrangement of spaces Z₁And at least one space Z of nested tubular arrangement₂In the relationship of (A) to (B)₁＞1.2Z₂Alternatively, Z₁＞1.5Z₂Alternatively, Z₁＞2Z₂Alternatively, Z₁＞2.5Z₂。

In one embodiment, the fibers exhibit a phase birefringence of at least 1x10^-4。

In one embodiment, the fiber exhibits a loss of at most about 0.1 db/m, optionally at most about 0.01 db/m.

In one embodiment, the fibers exhibit a loss ratio between orthogonal polarizations of the fundamental modes of at least about 100, alternatively at least about 200, alternatively at least about 500, alternatively at least about 1000.

The invention also extends to the use of the above-described fibre as a polarisation maintaining fibre, optionally maintaining the input polarisation of the source signal.

The invention also extends to the use of the above fibre as a polarising fibre, optionally to introduce polarisation to the source signal, optionally to generate linearly polarised light from an unpolarised input.

The present invention has a number of areas of applicability, including:

optical data communication

The fibers of the present invention should be capable of guiding light with propagation losses below 0.15 db/km, which presents the fundamental physical limitations of existing telecommunications fibers and has a wider available bandwidth. Unlike all other hollow core fibers of the prior art, the fibers of the present invention also operate in an efficient single mode behavior, which is desirable to avoid inter-mode distortion in order to transmit data. By combining the ultra low loss with the non-linearity, which is typically three orders of magnitude lower than glass guide fibers, the present invention enables a significant improvement in transmission capacity over existing fibers.

Low latency transmission

Directing light in air provides 30% higher transmission speed than directing light in standard fibers, a feature that is particularly useful for algorithmic trading companies that require low latency.

Low latency may also be suitable in data center/supercomputer applications, where hundreds of thousands of meters of fiber optic cable are used for the interconnection of thousands of servers. The ability of the present invention to exhibit ultra-low loss at any given wavelength enables these ultra-low delay fibers to operate at wavelengths of-0.8 microns, which is often used as an interconnect in data centers because it enables the use of cheaper Vertical Cavity Surface Emitting Laser (VCSEL) transmission technologies.

Radiation-resistant

The fibers of the present invention provide radiation resistance, which is of great interest in the transmission of data synchronization signals in high energy physical experiments and in the space mission, where operation at mid-infrared wavelengths (mid-IR) is an additional requirement.

High power delivery

The fibers of the present invention can be configured such that less than 0.1% of the optical power, and in some configurations less than 0.01% of the optical power, is directed in the glass, and the Mode Field Diameter (MFD) is easily modified to any wavelength required for fiber laser operation, e.g., 0.8 microns, 1 micron, 1.55 microns, and 2 microns. The fibers also have a flexural rigidity which is significantly superior to any solid fiber having a similar effective area and which is effectively unimodulated. These characteristics make the inventive fiber suitable as a power transmission fiber for use in industrially produced high power fiber lasers, in particular pulsed operation, involving peak powers that induce detrimental nonlinear spectral broadening and transient pulse distortions, or possibly even exceeding the damage threshold of the material. The large simplification in cross-sectional complexity compared to photonic band gap fibers would enable arrays of these fibers to be stacked to deliver undistorted, ultrashort, high peak power pulses from multiple laser sources for continuous coherent recombination, which would be useful in laser-driven particle acceleration applications.

Mid-infrared (Mid-IR) gas spectroscopy

The fibers, optical power and glass of the present invention have very little overlap (typically at 10)^-5And 10^-4In between) capable of transmitting light at wavelengths at which the glass is highly opaque. This feature, in combination with directing light in a gaseous medium, enables the fibers of the present invention to be used in mid-infrared spectroscopy applications where there is fundamental rotational vibration absorption of most molecules. Further applications include gas sensors, e.g. in cancer screening studiesIn a fine breath analysis. When made of fused silica, the fibers of the present invention should be capable of transmission with-db/meter loss at wavelengths as high as 6-6.5 microns. Furthermore, unlike photonic band gap fiber technology, the present invention can be applied to higher index glasses that are more transparent in the mid-infrared, allowing for potential transmission at wavelengths up to 10 microns or more.

Biomedical applications

The fibers of the present invention provide low loss guidance of high energy pulses at specific mid-infrared wavelengths, making the fibers of the present invention useful in surgical applications. For example, wavelengths on the order of 3 microns are currently used to ablate large amounts of biological tissue due to their high absorption by water present in the tissue. The high fluence normally required for tissue ablation makes it impossible to use solid fibers, and existing hollow fibers typically suffer from high bending losses, which the present invention can overcome. Furthermore, the invention enables applications at shorter wavelengths, typically 0.8 to 1 micron, enabling use in endoscopy, enabling the transmission of intense pump pulses for molecular nonlinear detection, for example in clinical assessment of cancer cell growth, or in real-time studies of cellular processes in vivo.

Gyroscope and temperature insensitive fiber for delivering accurate frequency/time information

The fibers of the present invention, having optical modes that travel mostly through air, will have much smaller kerr, faraday and thermal constants than silicon, show much lower dependence on power, magnetic field and temperature fluctuations. These characteristics are particularly useful in gyroscopes and in appropriate applications for temperature insensitive fibers used to deliver ultra-precise time stamps.

In the following, preferred embodiments of the invention will be described by way of example only with reference to the accompanying drawings, in which:

FIG. 1 shows a hollow core anti-resonant fiber according to a first embodiment of the invention;

FIG. 2 shows a profile curve of the strength of the primary air-guiding mode of the fiber according to FIG. 1;

FIG. 3 shows loss curves associated with different nested tubular element arrangements for a comparison fiber and the fiber according to FIG. 1, with overlapping, just-in-contact (zero spacing) and spaced configurations, the d/t ratios being-0.5, -0.3, -0.1, 0, 0.8, 1, 2 and 4 as a function of wavelength;

FIG. 4 presents the losses as a function of the d/t ratio for a comparative fiber and a fiber according to FIG. 1 at two embodied wavelengths, i.e., 1.4 microns and 1.6 microns;

fig. 5 shows the field strength in the azimuthal and radial directions of the fibre according to fig. 1 at the interface between adjacent second tubular elements;

FIG. 6 shows the loss as a function of wavelength for the fiber according to FIG. 1;

fig. 7 shows the loss as a function of wavelength for a straight fiber according to the fiber of fig. 1, the core radius R of which is 13, 15, 20 and 25 micrometers;

fig. 8 shows the losses of the Fundamental Mode (FM) and the first Higher Order Mode (HOM) of the fiber according to fig. 1;

FIG. 9 shows loss curves for the fiber-based mode HE11 and the lowest loss high-order mode TE01 according to FIG. 1;

FIG. 10 shows another loss curve for the fiber-based mode HE11 and the lowest loss high-order mode TE01 according to FIG. 1;

FIG. 11 shows a plot of differential loss as a function of z/R ratio for the fiber-based mode HE11 and the lowest loss high-order mode TE01 according to FIG. 1;

FIG. 12 shows the loss curves as a function of wavelength for the fiber according to FIG. 1, with six and eight nested tubular elements;

FIG. 13 shows loss curves for the Fundamental Mode (FM) and the first Higher Order Mode (HOM) of the fiber according to FIG. 1, with six and eight nested tubular elements;

FIG. 14 shows the loss curves as a function of wavelength for the fiber according to FIG. 1, with Mode Field Diameters (MFD) of (I)9 microns, (II)13 microns, and (III)16 microns;

FIG. 15 shows the loss curves as a function of wavelength for a comparative fiber and the fiber according to FIG. 1, each fiber having a Mode Field Diameter (MFD) of 9 microns;

FIG. 16 shows a hollow core anti-resonant fiber according to a second embodiment of the present invention;

FIG. 17 shows the loss curves as a function of wavelength for the fibers according to FIGS. 1 and 16, both straight (solid line) and curved (dashed line) to a fiber radius of 2.5 cm;

FIG. 18 shows a hollow core anti-resonant fiber according to a third embodiment of the present invention;

FIG. 19 shows a hollow core anti-resonant fiber according to a fourth embodiment of the present invention;

FIG. 20 shows a hollow core anti-resonant fiber according to a fifth embodiment of the present invention;

FIG. 21 shows a hollow core anti-resonant fiber according to a sixth embodiment of the present invention;

FIG. 22 shows a hollow core antiresonant fiber in accordance with a seventh embodiment of the present invention;

FIG. 23 shows a hollow core anti-resonant fiber according to an eighth embodiment of the present invention;

FIG. 24 presents a cross-section of a substantially anti-crossing mode of the fiber of FIG. 23;

FIG. 25 shows a hollow core antiresonant fiber in accordance with a ninth embodiment of the invention;

FIGS. 26(a) and (b) show the modal intensity profile and electric field direction for high-loss (y-polarization) and low-loss (x-polarization) perpendicular polarization, respectively, of the fiber-based mode of FIG. 25;

fig. 27(a) to (c) show Phase Birefringence (PB), loss and loss ratio, respectively, as a function of wavelength ranging between 1.5 microns to 1.6 microns for the fiber of fig. 25.

Figure 1 shows a hollow core anti-resonant fibre according to a first embodiment of the present invention.

The fibre comprises a first tubular cladding element 1, a plurality of second tubular elements 5 and a plurality of third tubular elements 7, the first tubular cladding element 1 defining an inner cladding surface 3, the plurality of second tubular elements 5 being arranged spaced apart at the cladding surface 3, in this embodiment being symmetrical, and together defining a core 9 of radius R, each of the plurality of third tubular elements 7 being nested in a respective one of the second tubular elements 5, whereby the nested second and third

tubular elements

5, 7 provide a nested tubular arrangement 11 a-f.

In this embodiment the cross-section of the

tubular elements

1, 5, 7 is circular, but other tubular shapes are possible, for example, substantially square, rectangular, elliptical or oval.

In this embodiment, the

tubular elements

1, 5, 7 each have the same cross-sectional shape, but one or more of the

tubular elements

1, 5, 7 may also have a different cross-sectional shape.

In this embodiment the

tubular elements

1, 5, 7 are circular and have full rotational symmetry, but in other embodiments radially elongated structures are possible, showing reflection symmetry about a single plane or two perpendicular planes.

In this embodiment the

tubular elements

1, 5, 7 are made of glass, here silicon.

In this embodiment, the second tubular element 5 is attached to the first tubular element 1 at only a single location of the cladding surface 3.

In this embodiment the second tubular elements 5 are arranged in a non-contacting relationship with a spacing d between adjacent second tubular elements 5.

In this embodiment, the ratio d/t of the spacing d of adjacent second tubular elements 5 and the wall thickness t of the second tubular elements 5 is greater than about 0.5, optionally greater than about 0.8, optionally greater than about 1, and optionally greater than about 2, and less than about 12, optionally less than about 10, optionally less than about 8, and optionally less than about 6.

In this embodiment, the third tubular elements 7 are each attached to a respective second tubular element 5 at the location where the second tubular element 5 is attached to the envelope surface 3.

In this embodiment, the second and third

tubular elements

5, 7 have the same or substantially the same wall thickness t.

In this embodiment, the diameter difference z between the second and third

tubular elements

5, 7 is such that the ratio z/R between the diameter difference z and the core radius R is between about 0.3 and about 1.0, optionally between about 0.35 and about 0.95, providing an optimum for the lowest fundamental mode loss.

The inventors have also surprisingly determined that an arrangement with nested

anti-resonant elements

5, 7 and by providing a defined relationship between the spacing d of adjacent second tubular elements 5 and the wall thickness t of the second tubular elements 5, which allows a non-contacting relationship of the second tubular elements 5, a fiber is obtained which is capable of significantly reducing losses compared to existing fibers.

The fiber of the present invention provides a nodeless arrangement of anti-resonant legs at the core 9, confining the light with a wide bandwidth, and the third tubular element 7 also provides an additional boundary layer, which acts consistently like a bragg mirror, which significantly reduces the confinement loss of the fiber. The effect of the node-free arrangement and nesting of the third tubular element 7 is clearly shown in fig. 2, comprising a 3 db profile curve of the density of the primary air guiding modes. With this arrangement, all of the inner layer boundaries within the fibre operate at anti-resonance and the only nodes within the fibre are located at the boundaries of the outer cladding element 1 where the field is typically 60-80 db lower than the field at the core 9.

Figure 3 shows the loss curves associated with different arrangements of nested

tubular elements

5, 7, with overlapping, just touching (zero spacing) and spaced configurations, the d/t ratio, as a function of the core radius R being 15 microns, the wall thickness t of the second tubular element 5 being 0.42 microns, and the z/R ratio being-0.5, -0.3, -0.1, 0, 0.8, 1, 2 and 4 for the wavelength of the fibre of 0.9. The negative ratio of d/t assumes an arrangement in which the second tubular elements 5 are in overlapping relationship. As can be seen in fig. 2, fibers with optimized ratios d/t show significantly reduced losses over a wide bandwidth range, particularly over the wavelength range from about 1.2 microns to about 1.8 microns.

Fig. 4 presents the losses as a function of the d/t ratio of the fiber with a core radius R of 15 microns, a wall thickness t of the second tubular element 5 of 0.42 microns, and a z/R ratio of 0.9 at two embodied wavelengths, i.e. 1.4 microns and 1.6 microns. These curves clearly show the significant improvement in losses when using nested

tubular elements

5, 7 and a limited range of d/t ratios.

As can be observed, the losses increase significantly when the second tubular element 5 is in contact or the d/t ratio reaches 0. Fig. 5 shows the field strength in the azimuthal and radial directions at the intersection between adjacent second tubular elements 5. When the second tubular element 5 is in contact (d/t ≦ 0), the field is disturbed, but the disturbance in the azimuthal direction and the disturbance in the radial direction do not match, because there is a thicker waveguide, making the waveguide ineffective in anti-resonance. Also, when the second tubular elements 5 are spaced apart, but the spacing is small relative to the wall thickness t, the field between the second tubular elements 5 is locally enhanced due to the discontinuity of the normal electric field components. And, when the d/t ratio is too large, the nested

tubular elements

5, 7 will be too far apart to act as effective waveguides and prevent leakage. Only if the nested arrangement of the

tubular elements

5, 7 meets certain conditions and has a selected d/t ratio, the nested

tubular elements

5, 7 provide a waveguide sufficient for anti-resonance to effectively repel the field from the inner tubular channel.

Fig. 6 shows the losses of the seven fibers as a function of wavelength, respectively, (I) a core radius of 7 microns and a wall thickness of the second tubular element 5 of 0.2 microns, (II) a core radius of 11 microns and a wall thickness of the second tubular element 5 of 0.3 microns, (III) a core radius of 15 microns and a wall thickness of the second tubular element 5 of 0.42 microns, (IV) a core radius of 20 microns and a wall thickness of the second tubular element 5 of 0.55 microns, (V) a core radius of 27 microns and a wall thickness of the second tubular element 5 of 0.6 microns, (VI) a core radius of 54 microns and a wall thickness of the second tubular element 5 of 1 micron, (VII) a core radius of 80 microns and a wall thickness of the second tubular element 5 of 2.25 microns, the z/R ratio being 0.9. The solid line shows limiting losses and material absorption losses, both of which are dominant losses for most fibers at wavelengths of 2 microns and longer, while the dashed line shows scattering losses, only associated with fibers guided at short wavelengths.

As observed, losses from Ultraviolet (UV), through visible light, up to a wavelength of about 2.5 microns, can be expected to be on the order of 1 decibel/kilometer or less. It is still possible for the loss to be less than 1 db/m up to about 5 microns, and fibers with losses of about 2 db/m to about 4 db/m can be used up to 7 microns. In contrast, the photonic band gap fiber has a minimum transmission loss window centered between 1.5 and 2 microns at the near Infrared (IR).

In addition, in the fibers of the invention, the fraction of guided optical power in the glass is particularly low (at 10)^-5To 10^-4In between) which allows light to be transmitted at wavelengths at which the glass is highly opaque. For example, in the case of silica glass, only fibers with very little db/m loss can be guided over a wavelength range of about 5 microns to about 7 microns, when the glass loss is 60000 db/m. The light directing mechanism of the present invention also enables the use of glass with higher refractive index and longer infrared phonon edges, thus enabling hollow fibers to be directed at wavelengths up to 10 microns, longer to 12 microns, and possibly even at 15 microns. Again, it is emphasized that the case of photonic band gap fibers is that high refractive index glass severely affects performance compared to photonic band gap fibers, so that the appearance of guided photonic band gap fibers made of glass other than silicon has not been reported to date.

Fig. 7 shows the losses as a function of wavelength, the core radius R of the straight fibers in fig. 7 being 13, 15, 20 and 25 microns, the d/t ratio being 5, the wall thickness t of the second tubular element 5 being 0.55 microns, and the z/R ratio being 0.9, in contrast to a typical antiresonant fiber (ARF) (2011 european optical communication conference (ECOC) paper mo.2.lecervin.2, the performance of Poletti et al, "optimized hollow antiresonant fibers" (PBGF) in the state of the art) (2013, volume 7, natural communication, pages 279 to 284, Poletti et al), and a conventional fiber with the lowest loss (2002, volume 38, electronic promo, pages 1168 to 9, Nagayama et al, ultra low loss (1484 kilo m/db), and the extension of the pure silica fiber 1163).

As observed, the core radius R increases, the loss decreases, and the decrease in loss has been modeled as λ⁷/R⁸Where λ is the wavelength. With a core radius of 13 microns, the minimum loss of the fiber of the present invention is equivalent to state-of-the-art Photonic Band Gap Fibers (PBGF) and can operate over a wider bandwidth range. Core radius of 20 microns, the inventionAgain, it can operate over a wider bandwidth range, especially at longer wavelengths.

In this embodiment, the fibre comprises six nested

tubular elements

5, 7. In other embodiments, the fiber may comprise three, four or five nested

tubular elements

5, 7.

This arrangement, contrary to the understanding adopted in the prior art (vol. 18, optical express 23133 to 23146, Vincetti et al), requires seven or eight tubular elements or waveguides to optimize performance, especially in the extinction of high order modes.

In addition to the benefits associated with loss and bandwidth, the fibers of the present invention are also effectively unimodulated.

Fig. 8 shows the losses of the Fundamental Mode (FM) and the first Higher Order Mode (HOM), the core radius R of the fiber in fig. 8 being 25 micrometers, the d/t ratio being 5, the second tubular element 5 having a wall thickness t of 0.55 micrometers, and the z/R ratio being 0.9. A two order of magnitude difference in loss shows effective single mode performance over a sufficiently long fiber. This single mode presents a distinct advantage for data transmission in that data distortion from inter-mode coupling is avoided, as compared to Photonic Band Gap Fibers (PBGFs), which, although successfully used as an exemplification for high data capacity transmission, are inherently multi-modal and have relatively low differential mode losses, only approximately 2 times, which presents problems for use in mode-division multiplexing.

Fig. 9 shows the loss curves for the fundamental mode HE11 and the lowest-loss high-order mode TE01, the fiber core radius in fig. 9 being 15 microns, the wall thickness t of the nested

tubular elements

5, 7 being 0.42 microns, the d/t ratio being 5, and the z/R ratio being 0.8.

As observed, the differential loss of the fundamental mode HE11 and the lowest-loss high-order mode TE01 is approximately an order of magnitude, facilitating single-mode operation. In addition, it is to be noted that the fraction of the optical power guided in the glass is very low (at 10)^-4To 10^-3In between).

Fig. 10 shows the loss curves for the fundamental mode HE11 and the lowest-loss high-order mode TE01, the fiber core radius in fig. 10 being 15 microns, the wall thickness t of the nested

tubular elements

5, 7 being 0.42 microns, the d/t ratio being 5, and the z/R ratio being 1.

As observed, the differential loss of the fundamental mode HE11 and the lowest-loss high-order mode TE01 is approximately two orders of magnitude, further contributing to single-mode operation. By increasing the z/R ratio, the differential losses are greatly increased by enhancing the resonant coupling at the nested

tubular elements

5, 7. In addition, it is again emphasized that the fraction of the optical power guided in the glass is very low (at 10)^-4To 10^-3In between).

Fig. 11 shows a plot of the differential loss of the fundamental mode HE11 and the lowest-loss high-order mode TE01 as a function of z/R ratio, the fiber core radius in fig. 11 being 15 microns, the nested

tubular elements

5, 7 having a wall thickness t of 0.55 microns and a d/t ratio of 5.

As can be seen, in this embodiment the fibre provides two effective single mode states, providing improved effective single mode operation, a z/R ratio of between about 0.05 and about 0.4, optionally between about 0.1 and about 0.3, more optionally between about 0.2 and about 0.3, wherein the high order modes LP01 within the core 9 match the modes LP11 present within the third tubular element 7, a z/R ratio of between about 0.8 and about 1.2, optionally between about 0.9 and about 1.2, more optionally between about 1.0 and about 1.2, wherein the high order modes LP01 within the core 9 match the modes LP11 guided between the second and third

tubular elements

5, 7. In these arrangements, the modes supported by the nested

elements

5, 7 have well-matched effective refractive indices (neff), optionally with an effective mode difference (Δ neff) of less than about 0.001 from the high order modes LP01 within the core 9, so as to cause coupling to the supported modes due to perturbations and thus increase the losses associated with the supported modes, thereby increasing the differential losses.

As can also be seen, in this embodiment, the fibers provide the lowest fundamental loss for a z/R ratio of between about 0.35 and about 0.9.

Fig. 12 shows the losses as a function of wavelength, the first fibre in fig. 12 having six nested

tubular elements

5, 7, the core radius R being 15 microns, the wall thickness of the

tubular elements

5, 7 being 0.42 microns, the d/t ratio being 5 and the z/R ratio being 0.9, the second fibre having eight nested

tubular elements

5, 7, the core radius R likewise being 15 microns, the wall thickness of the

tubular elements

5, 7 being 0.42 microns, the d/t ratio being 5 and the z/R ratio being 0.7, the third fibre having eight nested

tubular elements

5, 7, the core radius R being 15 microns, the wall thickness of the

tubular elements

5, 7 being 0.42 microns, the d/t ratio being 18 and the z/R ratio being 0.5.

As can be observed, a fibre with six nested

tubular elements

5, 7 has a significant advantage in terms of losses.

Fig. 13 shows the loss curves for the fundamental FM and the first higher-order HOM modes, one fiber in fig. 13 having six nested

tubular elements

5, 7, a core radius R of 15 microns, a wall thickness of the

tubular elements

5, 7 of 0.42 micron, a d/t ratio of 5 and a z/R ratio of 0.9, one fiber having eight nested

tubular elements

5, 7, a core radius R of 15 microns, a wall thickness of the

tubular elements

5, 7 of 0.42 micron, a d/t ratio of 18 and a z/R ratio of 0.5.

As can be observed, the differential loss between the fiber-based mode FM and the first higher-order mode HOM with eight nested

tubular elements

5, 7 is only 2.5, whereas the differential loss between the fiber-based mode FM and the first higher-order mode HOM with six nested

tubular elements

5, 7 is 50, so that improved mode control and efficient single-mode guiding can be achieved by propagating the modes over a sufficiently long distance range within the inner layer of the fiber.

In addition, the fibers of the present invention allow for fine control of the Mode Field Diameter (MFD) at any given wavelength, enabling the fabrication of hollow core fibers whose mode field diameter matches that of the solid core counterpart. In contrast, in a photonic band gap fiber, for a given operable wavelength, a fixed set of core sizes can only be obtained by removing an integer number of capillaries to form a central core.

Fig. 14 shows the operation of three fibers having Mode Field Diameters (MFDs) of (I)9 microns, (II)13 microns, and (III)16 microns at the operable wavelength of 1.06 microns typical for ytterbium-doped fiber lasers. All three fibres have six nested

tubular elements

5, 7 with a wall thickness t of 0.375 micron, a d/t ratio of 5 and a z/R ratio of 0.7, the only difference being the core radius R, the core radius R of the first fibre (I) being 6 micron, the core radius R of the second fibre (II) being 8 micron and the core radius R of the third fibre (III) being 10 micron.

As observed, even at the smallest mode field diameter, in this embodiment, the fiber has sufficiently low losses for power delivery applications. For example, adjusting the mode field diameter to coincide with that of a solid state active/passive fiber from a fiber laser, such as an ytterbium fiber laser, minimizes coupling losses and facilitates direct splicing, while ultra-low nonlinearities ensure very high nonlinearities and damage thresholds, which are particularly desirable in short pulse delivery applications.

Furthermore, the fibers can be tightly wound and exhibit an equivalent low loss value. As shown in fig. 14, the total loss when the first mode field diameter fiber (I) was wound up around a 1 cm diameter mandrel was equivalent to the loss when the fiber was straight. These loss characteristics can be compared to those of the prior art hollow core design with a mode field diameter of 9 microns operating at 1.06 micron wavelength, which shows significantly higher losses, as shown in figure 15.

Fig. 16 shows a fibre according to a second embodiment of the invention.

The fibre in this embodiment is similar to the fibre in the first embodiment described above, except that there are fourth tubular elements 15, the fourth tubular elements 15 being nested in corresponding third tubular elements 7, respectively.

In this embodiment, the second, third and fourth

tubular elements

5, 7, 15 have the same or substantially the same wall thickness t.

Fig. 17 shows the loss curves as a function of wavelength for the fibers of the first and second embodiments described above, both straight (solid line) and curved (dashed line), with a radius of curvature of 2.5 cm in this example.

As can be observed, the introduction of the additional tubular element 15 in the second embodiment described above allows to significantly reduce the losses, and moreover, the second embodiment described above shows a significant reduction of the differential losses upon bending.

Fig. 18-22 show fibers according to further embodiments of the present invention.

Fig. 18 is a variant of the first embodiment described above, comprising second and third

tubular elements

5, 7 of different shapes, in this embodiment an asymmetrical shape, here elliptical or oval. In this embodiment, the

tubular elements

5, 7 have a longer dimension in the radial direction of the cladding element 1. In this example, the z/R ratio of the fibers is 1.

In alternative embodiments, the

tubular elements

5, 7 may have different cross-sections. For example, the second tubular element 5 may be radially stretched, such as elliptical or oval, and the third tubular element 7 is circular.

Figure 19 is a further variant of the first embodiment described above, in which the cladding element 1 has a different tubular shape, in this embodiment, substantially square, surrounding the second and third

tubular elements

5, 7, and comprising four nested tubular arrangements 11 a-d.

Figure 20 is a further variation of the first embodiment described above, including an additional tubular anti-resonant element 17, the tubular anti-resonant element 17 being intermediate the respective nested

tubular elements

5, 7.

Figure 21 is a further variant of the first embodiment described above, comprising eight nested tubular arrangements 11a-h, the eight nested tubular arrangements 11a-h being arranged spaced apart from each other on the cladding surface 3 of the cladding element 1.

Fig. 22 is a variant of the second embodiment described above, comprising third and fourth

tubular elements

7, 15, having a larger diameter with respect to the second tubular element 5. In this embodiment, the resonance occurs between the higher order modes guided within the core 9 and the supported modes within the fourth, smallest element 15, which necessarily results in high losses in the supported modes.

Fig. 23 shows a fiber according to an eighth embodiment of the invention.

The fibre in this embodiment is structurally similar to the fibre in the second embodiment described above, except that there are four nested tubular arrangements 11a-d, each comprising a second, third and fourth

tubular element

5, 7, 15 arranged in perpendicular relationship to the first pair of tubular arrangements 11a, c and the second pair of tubular arrangements 11b, d. In alternative embodiments, the fibers may comprise a different number of nested tubular arrangements 11, for example, three, five, six, seven or eight nested tubular arrangements 11.

In this embodiment, the wall thickness t of the outer tubular element 5 of a pair of nested tubular arrangements, here the second pair 11b, d₁Different from the wall thickness t of the other outer tubular elements 5₂Here, the first pair of nested tubular arrangements 11a, c has the wall thickness t of the outer tubular element 5 of the above pair of nested tubular arrangements 11b, d₁Causing operation to be provided at anti-resonance, and the wall thickness t of the outer tubular element 5 of the other pair of nested tubular arrangements 11a, c₂Facilitating operation at the resonant edge.

As with the embodiment described above, the structure of this embodiment reduces the Confinement Loss (CL) by providing a reflective antiresonant layer from the inner

tubular elements

7, 15 of the nested tubular arrangements 11a-d and reducing the glass node in the cladding structure, but significantly, the wall thickness t of the outer tubular element 5 through the pair of nested tubular arrangements 11b, d₂And provides operation at the resonant edge, introduces strong Phase Birefringence (PB) for the fundamental mode vertical Offset (OPFM) by introducing an effective refractive index difference in the direction of the pair of nested tubular arrangements 11b, d.

FIG. 24 shows a base mould section of the above-mentioned fibre, through the wall thickness t of the outer tubular element 5 based on each pair of nested tubular arrangements 11a-d₁And t₂The difference of (2) is obtained by modulo inversion crossing.

In one embodiment, the wall thickness t of the outer tubular elements 5 of a pair of nested tubular arrangements 11b, d₁And the wall thickness t of the outer tubular elements 5 of the other pair of nested tubular arrangements 11a, c₂Is in the relationship of 0.5t₂＜t₁＜t₂Or 1.5t₂＞t₁＞t₂Alternatively, 0.4t₂＜t₁＜t₂Or 1.4t₂＞t₁＞t₂Alternatively, 0.3t₂＜t₁＜t₂Or 1.3t₂＞t₁＞t₂And optionally, t₁＜0.9t₂Or t₁＞1.1t₂。

In this embodiment, the wall thickness t of the outer tubular elements 5 of a pair of nested tubular arrangements 11b, d₁Is 1.42 μm, the wall thickness t of the outer tubular element 5 of the other pair of nested tubular arrangements 11a, c₂Is 1.172 microns.

In one embodiment, the core radius R is at most about 15 times, optionally at most about 7 times, optionally at most about 5 times the signal wavelength λ, wherein preferably the wavelength λ is about 0.5, 0.8, 1.06, 1.55, and 2 microns.

In this embodiment, the core radius R is 7 microns.

In this embodiment the wall thickness of the inner

tubular elements

7, 15 of the nested tubular arrangements 11a-d is 1.172 microns, the spacing of the nested tubular arrangements 11a-d, and the inter-tubular spacing Z between the

tubular elements

5, 7, 15 is 0.65R.

In this example, the fiber achieved 1.54x10^-4Is comparable to conventional solid polarization maintaining fibers and has a loss of about 0.01 db/m at 1.55 μm, which is excellent for hollow core fibers having such a small core.

Fig. 25 shows a fiber according to a ninth embodiment of the invention.

The fibres in this embodiment are similar in structure to the fibres in the eighth embodiment described above, with the difference that the cross-sectional size and/or shape of at least one

tubular element

5, 7, 15 of another pair of nested tubular arrangements 11a, c, perpendicular to the pair of nested tubular arrangements 11b, d, is different from the cross-sectional size and/or shape of at least one

tubular element

5, 7, 15 of the corresponding pair of nested tubular arrangements 11b, d.

In this embodiment, one of the inner

tubular elements

7, 15 of the other pair of nested tubular arrangements 11a, c, here the innermost tubular element 15, has a different cross-sectional dimension, whereby the spacing Z between one innermost tubular element 15 of the other pair of nested tubular arrangements 11a, c and the adjacent tubular element 7₁Between an innermost tubular element 15 and an adjacent tubular element 7 of the corresponding pair of nested tubular arrangements 11b, d of the above pairSpacing Z₂Different.

In this embodiment, the innermost tubular elements 15 of the other pair of nested tubular arrangements 11a, c are dimensioned such that the spacing Z between those innermost tubular elements 15 and the adjacent tubular elements 7₁Is 1.74R.

In this embodiment, the spacing Z of the other pair of nested tubular arrangements 11a, c₁And the spacing Z of the pair of nested tubular arrangements 11b, d above₂In the relationship of (A) to (B)₁＞1.2Z₂Alternatively, Z₁＞1.5Z₂Alternatively, Z₁＞2Z₂Alternatively, Z₁＞2.5Z₂。

With this configuration, the pair of nested tubular arrangements 11b, d act in one direction of those nested tubular arrangements 11b, d, maintaining polarization by means of the differently sized outer tubular elements 5 of those nested tubular arrangements 11b, d, and the other pair of nested tubular arrangements 11a, c act in a perpendicular direction to the other, those tubular arrangements 11a, c, obtaining matching between the core and cladding guided modes, thereby placing the coupled core field into those tubular arrangements 11a, c, thereby introducing large losses in the other direction, and introducing a single polarization to the source signal.

FIGS. 26(a) and (b) show the mode intensity profile and electric field direction for high-loss (y-polarization) and low-loss (x-polarization) orthogonal polarizations, respectively, for the fiber-based mode of FIG. 25.

As shown, the fibers in this embodiment exhibit surprising and significant optical properties with a fairly broad spectral range, high birefringence, low fundamental mode loss, and a large loss differential extending across the entire C-band to the first half of the L-band.

In the fibre in this embodiment, the slightly different mode size of one polarisation in one direction results from the different thicknesses of the outer tubular elements 5 of the pair of nested tubular arrangements 11a-d preventing coupling to cladding modes and keeping losses low, whereas in vertical polarisation, by contrast, the core-to-cladding out-coupling process introduces much larger losses and introduces a single polarisation to the source signal.

As can be seen, the phase birefringence is comparable to that of a conventional solid polarization maintaining fiber, having a wavelength of 1.4x10 between 1.5 and 1.6 microns^-4And 1.7x10^-4Relatively small variations in between.

As can also be seen, the loss of the lowest loss polarization is as low as about 0.0076 db/m at 1.55 microns. Although this loss is greater than in the eighth embodiment described above, this increase in loss can be offset by much greater losses for other polarizations, about 70 db/m at 1.55 microns, with a loss ratio between polarizations in the fundamental mode of up to about 1000. Due to this loss, the fiber will exhibit a single polarization, even in meter-scale applications.

The fibers in this embodiment exhibit an anti-resonant fiber structure that provides polarization retention and polarization functionality that has not heretofore been available.

Finally, it should be understood that the present invention has been described in terms of preferred embodiments and can be modified in numerous different ways without departing from the scope of protection of the invention as defined by the appended claims.

Claims

1. An anti-resonant hollow fiber comprising a first tubular element, a plurality of second tubular elements and a plurality of third tubular elements, the first tubular element being a cladding element, the A first tubular element defines an inner cladding surface, the plurality of second tubular elements are attached to the inner cladding surface and together define a core having an effective radius, the second tubular elements are spaced apart and Adjacent said second tubular elements are spaced apart, and each of said plurality of third tubular elements is respectively nested within a respective said second tubular element to provide a nested tubular arrangement, wherein , the first ratio of the interval between the adjacent second tubular elements and the wall thickness of the second tubular element is greater than 0.5 and less than 12, and the radial inner walls of the second tubular element and the third tubular element The second ratio of the radial spacing to the radius of the core is between 0.35 and 0.95.

2. The fiber of claim 1, wherein the nested tubular arrangement is arranged in a symmetrical relationship at the inner cladding surface.

3. The fiber of claim 1, wherein the cross-section of the first tubular element is circular.

4. The fiber of claim 1, wherein the cross-section of the second tubular element is circular.

5. The fiber of claim 1, wherein the second tubular element has a longer radial dimension than a tangential dimension.

6. The fiber of claim 5, wherein the cross-section of the second tubular element is elliptical or oval.

7. The fiber of claim 1, wherein one or more of the first tubular element, the second tubular element, and the third tubular element have different cross-sectional shapes.

8. The fiber of claim 1, wherein the first tubular element, the second tubular element, and the third tubular element are made of glass or silicon.

9. The fiber of claim 8, wherein the first tubular element, the second tubular element and the third tubular element are made of glass or silicon having an index of refraction of at least 1.4.

10. The fiber of claim 9, wherein the refractive index is 1.4 to 3.

11. The fiber of claim 9, wherein the refractive index is 1.4 to 2.8.

12. The fiber of claim 1, wherein each of the second tubular elements is attached to the first tubular element at only a single location on the inner cladding surface.

13. The fiber of claim 12, wherein the third tubular element is attached to the corresponding second tubular element at the location where the second tubular element is attached to the inner cladding surface.

14. The fiber of claim 1, wherein the first ratio is greater than 0.8.

15. The fiber of claim 14, wherein the first ratio is greater than one.

16. The fiber of claim 14, wherein the first ratio is greater than 2.

17. The fiber of claim 1, wherein the first ratio is less than 10.

18. The fiber of claim 17, wherein the first ratio is less than 8.

19. The fiber of claim 17, wherein the first ratio is less than 6.

20. The fiber of claim 1, wherein the second tubular element and the third tubular element have substantially the same wall thickness.

21. The fiber of claim 1, wherein the fiber has a fundamental loss of less than 0.15 dB/km at wavelengths between 1.0 microns and 2.5 microns.

22. The fiber of claim 1, wherein the fiber has a base loss of 1 dB/km at wavelengths up to 2.7 microns.

23. The fiber of claim 1, wherein the fiber has a fundamental loss of less than 1 dB/meter at wavelengths up to 5 microns.

24. The fiber of claim 1, wherein the fiber has a fundamental loss of less than 4 dB/meter at wavelengths up to 7 microns.

25. The fiber of claim 1, wherein the fiber has a fundamental loss of less than 1 dB/km at wavelengths down to 0.8 microns.

26. The fiber of claim 1, wherein the fraction of optical power directed by the fiber having the material of the second tubular element and the third tubular element is less than ^1x10-3 .

27. The fiber of claim 26, wherein the portion is less than 1 x ^10-4 .

28. The fiber of claim 1, wherein the core has a radius of less than 50 microns.

29. The fiber of claim 28, wherein the core has a radius of less than 40 microns.

30. The fiber of claim 28, wherein the core has a radius of less than 30 microns.

31. The fiber of claim 28, wherein the core has a radius of less than 25 microns.

32. The fiber of claim 28, wherein the core has a radius of less than 20 microns.

33. The fiber of claim 28, wherein the core has a radius of less than 15 microns.

34. The fiber of claim 28, wherein the core has a radius of less than 13 microns.

35. The fiber of claim 1, wherein the fiber exhibits an effective single mode.

36. The fiber of claim 35, wherein the differential loss between the fundamental mode and the lowest loss higher order mode is at least one order of magnitude.

37. The fiber of claim 36, wherein the differential loss is at least two orders of magnitude.

38. The fiber of claim 35, wherein the nested tubular arrangement supports modes having an effective index of refraction (neff) that is smaller than higher order modes in the core Difference (Δneff) of effective modes of 0.001.

39. The fiber of claim 1, wherein the fiber allows any mode field diameter (MFD) to be selected at any given wavelength.

40. The fiber of claim 39 in combination with a solid core fiber, wherein the hollow core fiber has a mode field diameter that matches the solid core fiber.

41. The fiber of claim 40, wherein the solid core fiber is directly bonded to the hollow core fiber.

42. The fiber of claim 40, wherein the solid core fiber is a fiber from a fiber laser.

43. The fiber of claim 1, wherein the difference in base loss when the fiber is straight and when the fiber is rolled to a diameter of 10 mm is less than two orders of magnitude.

44. The fiber of claim 43, wherein the difference is less than an order of magnitude.

45. The fiber of claim 43, wherein the difference is less than half an order of magnitude.

46. The fiber of claim 1, further comprising a plurality of fourth tubular elements, each fourth tubular element respectively nested within a corresponding third tubular element.

47. The fiber of claim 46, wherein the second, third, and fourth tubular elements have substantially the same wall thickness.